Problem Brief

Find Minimum Cost to Shift Machines

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There are n regions where some servers are hosted. The number of machines in the i^th region is machineCount[i], where 0 ≤ i < n. It can get difficult to manage all the different regions, so the team decided to move some machines to exactly 3 regions, where the number of machines in the i^th region is given by finalMachineCount[i], where 0 ≤ i < 3.

There are two operations that can be performed:

Add or remove a machine from any existing region. The number of computers in that server should be non-zero before and after the operation. This operation costs 1 unit.

Move all machines from one region to another existing region at a cost of shiftingCost units. The now empty region is destroyed in this operation.

Find the minimum cost to shift the machines so that any 3 regions have the counts required in finalMachineCount.

Note: It is possible that there are additional machines left at the end apart from the ones placed in the final 3 regions.

🩵 Thanks a squillion, spike! 🩵

1Example 1

Input

machineCount = [2, 4, 5, 3], finalMachineCount = [4, 4, 4], shiftingCost = 5

Output

Explanation

On increasing the number of machines of the 4^th region by 1 and decreasing the number of machines of the 3^rd region by 1, the new machineCount = [2, 4, 4, 4]. Total cost for these operations = 1+1=2. Use the 2^nd, 3^rd, and 4^th regions as the required servers, leaving behind the 1^st region.

2Example 2

Input

machineCount = [2, 3, 5, 7], finalMachineCount = [5, 10, 5], shiftingCost = 2

Output

Explanation

On increasing the number of machine in the 1st and 2nd regions by 1 and 2 machines respectively, the new machineCost = [2, 3, 5, 7]. Total cost for these operations = 1 + 2 = 3. Now, moving all the machines form th 4th region to 1st, which takes shiftingCost = 2, the new machineCost = [10, 5, 5]. The cost of this operation is 2. Therefore, the total cost = 3 +2 = 5 :) (Can confirm that the second example & explanation & constraints are accurate and original. I'm just being a bit lazy about uploading another source image atm :)

Constraints

Limits and guarantees your solution can rely on.

3 <= n <= 10

1 <= machineCount[i], finalMachineCount[i] <= 10^6

May missing 1 or more constraints here. Will add once find the reference :)